Trigonometry Definition and 664 Threads

Are there any well-written algebra 2 trig book that gives understandable contents for beginners?

Homework Statement Find the exact value of cos 247o+sin 293o Homework Equations trigonometry identities The Attempt at a Solution The furthest I can get is: cos 247o+sin 293o = cos 247o - cos 23o = -2 sin 135o sin 112o = -√2 cos 22o Then stuck...

Homework Statement Three cylinders are placed in contact with one another with their axes parallel. The radii of the cylinders are 3, 4 and 5 cm. An elastic band is stretched around the three cylinders so that the plane of the band is perpendicular to the axes of the cylinder...

Hi, I have the following equation : 2*sin3a=sqrt(2) I was able to solve it in a geometrical way(giving 6 solutions.) but I have no idea on how to solve it in a symbolic way...(which would take clearly less time to do ) Is there any way ? thank you

Homework Statement If the quadratic equation ax2+bx+c=0 has equal roots where a, b and c denote the lengths of the sides opposite to vertices A, B and C of a triangle ABC respectively, then find the sum of integers in the range of $$\left(\frac{\sin A}{\sin C}+\frac{\sin C}{\sin...

Homework Statement If $$\csc\frac{\pi}{32}+\csc\frac{\pi}{16}+\csc\frac{\pi}{8}+\csc\frac{\pi}{4}+\csc\frac{\pi}{2}$$ has the value equal to ##\cot\frac{\pi}{A}## then find A. A)61 B)62 C)63 D)64Homework Equations The Attempt at a Solution Writing cosec in terms of sin and taking the LCM to...

Homework Statement We know that sin(2⋅x)=2⋅sin(x)⋅cos(x)and cos(2x)=cos^2(x)−sin^2(x). Use the appropriate formula to expand cos(8x) in terms of one of these two formulas. Homework Equations sin(2⋅x)=2⋅sin(x)⋅cos(x) cos(2x)=cos^2(x)−sin^2(x) The Attempt at a Solution I am not...

How to determine the X coordinate of the red point if i know the Y coordinate and the angle between the adjacent side and the hypotenuse in the formed right triangle(see the image)? I don't know the length of the hypotenuse and the adjacent side of the triangle, i know only the angle between the...

f(x)=1+sinx what am I doing wrong here? 1+sin(-x)= 1-sin(x)

1) Are there any proofs that sine cosine and tangent are the same in all similar triangles? Like, that sine 30 degrees is the same no matter what the lengths are? Or is it just an axiom? 2) Is there a proof for the actual value for the sine cosine and tangent ratios (besides for common ones...

Homework Statement As ship is anchor off a long straight shoreline that runs north and south. From twi observation points. 15 miles apart on shore the bearings of the ship are N 31 ° E and S 53 ° E. What is the shortest distance from the ship to the shore. Homework Equations Sin θ Opp/...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

Homework Statement Two forces P and Q are applied to the lid of a storage bin as shown (see picture). Knowing that P = 48N and Q = 60N, determine by trigonometry the magnitude and direction of the resultant of the two forces. Homework Equations "The triangle method" where you put each...

Hi, I'm trying to start studying trig. again and I found some types of exercises that i have no idea how to solve can someone point me in the right direction? Sorry for the image size. In the first one I'm supposed to find the length of the smallest square knowing that the other two are 6 cm...

Homework Statement Simplify: [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x Homework Equations none The Attempt at a Solution [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x [(sec x)(sec2 x) - tan x (1 -1) sec x ] / sec2 x [(sec x)(sec2 x) - 0 ] /...

Homework Statement Dimensional Analysis: A displacement is related to time as: x = A sin (2∏ft), where A and f are constants. Find the dimensions of A. (Hint: a trigonometric function appearing in an equation must be dimensionless.) Homework Equations t = seconds The domain of a sine...

Homework Statement \phi = 4\arctan{\exp^{m\gamma(x-vt)}} Show \dot{\phi} = -2m\gamma v \sin{\frac{\phi}{2}} Homework Equations The Attempt at a Solution \phi = 4\arctan{\exp^{m\gamma(x-vt)}} \tan{\phi/4} = \exp^{m\gamma(x-vt)} \frac{\dot{\phi}}{4\cos^{2}{\frac{\phi}{4}}} =...

Homework Statement Which of the following is the solution set of the equation $$2\arccos(x)=\text{arccot}\left(\frac{2x^2-1}{2x\sqrt{1-x^2}}\right)$$ A)(0,1) B)(-1,1)-{0} C)(-1,0) D)[-1,1] Ans: A Homework Equations The Attempt at a Solution I start by rewriting LHS in terms of ##\arctan##...

Homework Statement The sum of the infinite terms of the series \text{arccot}\left(1^2+\frac{3}{4}\right)+\text{arccot}\left(2^2+\frac{3}{4}\right)+\text{arccot}\left(3^2+\frac{3}{4}\right)+... is equal to A)arctan(1) B)arctan(2) C)arctan(3) D)arctan(4) Ans: B Homework Equations The Attempt at...

A pulley with a radius of 10 inches uses a belt to drive a pulley with a radius of 6 inches. Find the angle through which the smaller pulley turns as the 10-inch pulley makes one revolution. State your answer in radians and also in degrees. can you rephrase the question for me. thanks!

Hey everyone, I was wondering if anyone had any thoughts on Gelfand's Trigonometry book. https://www.amazon.com/dp/0817639144/?tag=pfamazon01-20 I'm looking for a trigonometry supplement. I actually just finished taking trig over the summer, but my textbook(Larson's Trigonometry) does a...

For a triangle with sides a, b, c and angle C, where the angle C subtends the side c, show that c \geqslant (a+b) \sin \left( \frac C2 \right) _______ Let us stipulate 0^\circ < C < 180^\circ and of course a,b,c > 0. Consequently, 0^\circ < \frac C2 \leqslant 90^\circ \implies 0 < \sin^2...

Hello, Could you please help me with a problem that I saw in my exam? I have tried to solve it but end up getting one solution which is not correct. There happens to be 2 solutions to the problem which appear periodically. The problem has to be algebraically solved without the use of a...

I don't need unit circle proof or proof using trignometric equality. I know those. I am attaching a image. Please read it. It is from the book Plane Trigonometry by S L Loney. See what it says. I know that angle MOP = angle M'P'O and both triangles formed are congruent, OM' = MP and M'P" = OM...

Hi! I am currently taking a math class called college algebra. Here's the little description thing: MAC1105 - This course introduces the student to the concept of functions and their graphs. Students will graph linear, quadratic, rational, exponential, logarithmic, radical, power, and...

Homework Statement Hello everyone, I am having difficulty with something that should be very basic knowledge for most engineers here. I cannot see how this trigonometric relationship is being made from the phasor diagram I attached... I remember the SohCahToa rule, but it's just not...

Homework Statement An Antenna that is 90 feet high is on top of a hill. From a point at the base of the hill, the angles of elevation to the top and bottom of the antenna are 28.5° and 25°, respectively. To the nearest whole number of feet, how high is the hill? A, 189 ft B, 213 ft C...

I want to learn algebra 2 and trigonometry and was going to try to learn algebra 2 first then learn trigonometry after that. However after thinking I thought it would be more engaging to learn both at the same time. So my question is, should I learn algebra 2 first, then trigonometry, or...

Verify the compound angle formulae for; a) sin (20° + 30°) sin(A + B) = sinAcosB + cosAsinB sin(20°+30°) = (sin20°)(cos30°) + (cos20°)(sin30°) 0.76 = (0.34 x 0.87) + (0.94 x 0.5) 0.76 = 0.29+0.47 0.76 = 0.76 b) cos (30° + 40°) cos(A + B)...

A sinusoidal voltage is represented by the formula v = 6sin (314t + pi/2). Sketch the graph on the graph paper provided for values of t from 0.0s to 0.04s and show on the graph the values of • the amplitude • the time period and show how the frequency of the waveform may be determined from...

Question: "A cat sitting on the edge of a straight river bank spots a bird sitting in a tree directly across the river's edge. The angle of elevation from the cat to the bird is 15°. The cat the moves 25m along the river bank, and now spots the same bird at an angle of elevation of 13°. How...

From the equation, it implies: \left[\frac{\cos\left(\frac{\pi}{2}\cos\theta\right)}{\sin\theta}\right]^2=\sin^3\theta For the life of me, I have no idea how this come about. I don't even know where to start, this implies ##\cos\left(\frac{\pi}{2}\cos\theta\right)=\sin^{\frac 5 2}\theta##...

Homework Statement As per the attachment The Attempt at a Solution for a) sin58° = 32/hyp hyp*sin58°=32 hyp=32/sin58° hyp=32/0848 hyp=37.73 so to the nearest km between towns W & Y = 38km b)cosθ=adj/hyp cosθ=27/38 cosθ=0.710 θ=cos^-1(0.710) θ=44.76 so to the nearest...

Homework Statement In triangle PQR, the length of QR is 4 mm, the length of PR is 3.5 mm and the size of angle Q is 60°. What are the possible size(s) of angle P (to 2 decimal places) The possible solutions are 138.81, 81.79, 118.96, 61.04, 98.21 The Attempt at a Solution I've solved for...

Hello MHB, I am working with an old exam Solve this equation \sin^{-1}(x)+\cos^{-1}(2x)=\frac{\pi}{6} progress: I start take cos both side and I get 2x+cos(\sin^{-1}(x))=\frac{\sqrt{3}}{2} I draw it and call the bottom side for B and get so we got \sqrt{1-x^2}+2x=\frac{\sqrt{3}}{2} Is this...

Homework Statement http://imgur.com/x8D2wqO I need to solve for theta and I keep getting the angle 65, using cosine law and pythagorean theorem but the answer key says that the angle is 93. The diagram is not to scale. Is my answer wrong or is the answer key incorrect?

Homework Statement If cot (α + β) = 0 then sin(α +2β) is the options are a. sin α b. cos α c. sin β d. cos 2β Homework Equations There is as such no equation The Attempt at a Solution I did try to solve it but I kept arriving at the wrong answer. The correct...

Homework Statement \lim_{x \to \frac{\pi}{3}} \frac{1-2 cos x}{\pi - 3x} Homework Equations trigonometry identity properties of limit for trigonometry The Attempt at a Solution I have done several attempts but got me nowhere. I just need an idea to start. Thanks

Homework Statement \lim_{x \to 0} \frac{tan (cos 4x - 1)}{3x ~ sin (\frac{4}{3} x)} Homework Equations limit for trigonometry The Attempt at a Solution can I do it like this: \frac{tan (cos 4x - 1)}{3x ~ sin (\frac{4}{3} x)} = \frac{- tan (2 sin^{2} 2x)}{3x ~ sin (\frac{4}{3}...

The signal length from satellite to the Earth station (AC) can be found as 2(H)/[{sin^2(theta)+(2(H)/R)}^1/2+sin(theta)] Due to the Earth projection where "H" is satellite height and and R is the Earth radius My question is Can you help me to derive this equation? how they have...

The signal length from the satellite to the Earth station can be found as2(hs-he)/[{sin^2(theta)+(2(hs-he)/Re)}^1/2+sin(theta)] if theta < 5 degrees Due to the Earth projection where "hs" is satellite height and "he" is the Earth station height and Re is the Earth radius=3700 Km My question is...

Homework Statement Calculate the value of \tan(\frac{\pi}{12}) without the use of a calculator and showing all steps. Homework Equations Compound angle formula / Double angle formula The Attempt at a Solution Using an equilateral triangle of side length 2 I've shown that...

Hi! I am finding the work-energy principle and idea of total mechanical energy hard to apply to finding the work done against/by a particular force. For example in the question below, why is there no work done against the weight of the skier acting down the slope? Any help would be great! Thanks :D

Hi everyone, I've been looking for the finite sum formulae of trig functions. I've found the easiest ones (sine and cosine). But the one for the tangent seems to be very hard. No mathematical tricks work. Plus I've looked it up on the internet. Nothing. I will greatly appreciate your help...

Homework Statement we have sin(3x)=cos(2y) sin(x+pi/3)=cos(y-pi/3) solve in RxR Homework Equations The Attempt at a Solution i tried squaring both sides and turning everything to cos 2a then turning it into an XY=0 but that didn't help at all i ended up with y=0 which...

Homework Statement ∫xtan^-1(x^2)dx Homework Equations The Attempt at a Solution I did u = x, du = 1, v = ? ,dv = tan^-1(x^2)dx I do not know how to get the integral of tan^-1(x^2)

Homework Statement Making sure I got the right answer.Homework Equations The Attempt at a Solution

Homework Statement Hi guys, How can sin(∏)cos(ω∏)-cos(∏)sin(ω∏) = sin(ω∏)? please guide me trigonometry identity to apply with this? Homework Equations The Attempt at a Solution

Dear Everyone, I need some help for this general cubic equation. \[ax^3+bx^2+cx+d=0\]. First divide the equation by a \[x^3+b/ax^2+c/ax+d/a=0\] Let x=y-b/(3a) ... $$y^3+py+q=0$$ where $$p=c/a-(b/a)^2)/3;q=d/a-(b/a*c/a)/3+(b/a)^3/27$$ $$y=cos \theta$$ then i need to use the identity for...

I'm about to take a trig class and it's been a while since my last math class. I was wondering if you guys knew of any websites that have good trig study guides and study sheets? anything is appreciated! Thanks!